Unraveling Optical Polarization at Deep Microscopic Scales in Crystalline Materials

Nanophotonics, the study of light-matter interaction
at scales
smaller than the wavelength of radiation, has widespread applications
in plasmonic waveguiding, topological photonic crystals, superlensing,
solar absorbers, and infrared imaging. The physical phenomena governing
these effects can be described using a macroscopic homogenized refractive
index. However, the lattice-level description of optical polarization
in a crystalline material using a quantum theory has been unresolved.
Inspired by the dynamics of electron waves and their corresponding
band structure, we propose a microscopic optical band theory of solids
specifically applicable to optical polarization. This framework reveals
propagating waves hidden deep within a crystal lattice. These hidden
waves arise from crystal-optical indices, a family of quantum functions
obeying crystal symmetries, and cannot be described by the conventional
concept of refractive index. We present for the first time the hidden
waves and deep microscopic optical band structure of 14 distinct materials.
We choose Si, Ge, InAs, GaAs, CdTe, and others from Group IV, III–V,
and II–VI due to their technological relevance, but our framework
can be extended to a wide range of emerging 2D and 3D materials. In
contrast to the macroscopic refractive index of these materials used
widely today, this framework shows that hidden waves exist throughout
the crystal lattice and have unique optical polarization texture and
crowding. We also present an open-source software package, Purdue-Picomax,
for the research community to discover hidden waves in new materials
like hBN, graphene, and Moiré materials. Our work establishes
a foundational crystallographic feature to discover novel deep microscopic
optical waves in light-matter interaction.